Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

A worst case analysis of a dynamic programming-based heuristic algorithm for 2D unconstrained guillotine cutting

“…The sum of the running time of gcut1-gcut13 is 23 seconds from the work of Cintra et al (2008) and the sum of the running time of all the other instances except for UU1-UU3 and W1-W3 is 10,404.07 seconds from the work of Young-Gun et al (2003). In contrast, the running time of our DPH algorithm are 1.65 seconds and 42.62 seconds, correspondingly.…”

“…Meanwhile, Young-Gun et al (2003) have also proposed a best-first branch-and-bound algorithm based upon a bottom-up approach. Most recently, Cintra et al (2008) have also solved various kinds of cutting stock problems by using dynamic programming and column generation techniques. In solving the U_2DCP, the authors have further improved the dynamic programming approach proposed by Beasley (1985a) by reducing the size of sets of canonical dissections within L and W and by using more efficient computer programming techniques such as binary search.…”

“…For the instances gcut1-gcut13, both Beasley (1985a) and Cintra et al (2008) solved them to optimality. However, the work from Cintra et al (2008) was reported to have slightly less computational complexity than Beasley's (1985a). Thus we use Cintra et al's (2008) computer running time as a comparison.…”

“…All test problems have been used in various other papers (Beasley, 1985a;Cintra et al, 2008;Hifi, 1997;Morabito et al, 1992;Fayard et al, 1998;Alvarez-Valdes et al, 2002;Cui, 2007;Cui and Zhang, 2007;Young-Gun et al, 2003). They can be downloaded from http://www.laria.u-picardie.fr/hifi/OR-Benchmark/2Dcutting/.…”

“…Instances gcut1-gcut13 were taken from Beasley (1985a), which were tested later on by Cintra et al (2008). U1-U3 were from Hifi (1997).…”